Question

question find the value of tan s rounded to the nearest hundredth, if necessary. answer attempt 1 out of 6 tan s =

Explanation:

Step1: Find the adjacent side to angle S

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Let the adjacent side to angle S be \(x\). Given \(c = 50\) and one - side \(b = 40\). Then \(x=\sqrt{50^{2}-40^{2}}=\sqrt{(50 + 40)(50 - 40)}=\sqrt{90\times10}=\sqrt{900}=30\).

Step2: Recall the tangent formula

The tangent of an angle in a right - triangle is defined as \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For angle S, the opposite side to S is 40 and the adjacent side is 30. So \(\tan S=\frac{40}{30}=\frac{4}{3}\approx1.33\).

Answer:

1.33